Secular Spin-Orbit Dynamics in the Age of Exoplanets: The Moon as Reference and Guide

Abstract

The study of spin states of the Moon dates back to the 17th century when observations of the Moon were made by the Italian astronomer Giovanni Domencio Cassini. Following work allowed the generalization of these equilibrium states to other solar and extra-solar objects. Classic cases considered the equilibrium state of the spin vector of the Moon that is in resonance with the orbital motion for an orbit that is circular and undergoing uniform nodal precession. We are interested in generalizing this model of 1:1 spin-orbit resonance evolving on long timescales (and hence secular) to highly eccentric orbits in novel configurations including a) completely stationary orbits with neither apse nor nodal precessions (Laplace equilibrium), b) inclined, eccentric orbits with nodal precession (Kozai equilibrium), and c) inclined, eccentric orbits with apse precession (Evection resonance). On the other hand, this work includes a generalization on the shape of the body, extending the potential to an octupolar limit taking into consideration the asymmetry in the mass distribution of the Moon. The hypothetical configurations applied to the Moon will help complete the picture for the spin-orbit studies, providing solutions to possible systems to be discovered, in addition to setting the ground to further work that aims at a full numerical treatment of the problem.